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There is no homebrew formula for "Vim" but there is one for "MacVim" so you have to do $ brew install macvim instead.

Vim is already available on your Mac, in Terminal.app just type $ vim filename and hit <enter>. This version is a bit outdated and built with a limited feature set but, since you are new to Vim and programming, it's more than enough to get started.

Do $ vimtutor a couple of times to learn the basics before doing anything else with Vim.

Since you are new to programming, I'd suggest you do things progressively. Instead of using a package manager and the CLI right from the start why don't you simply download MacVim and work your way up from there?